230-0405/01 – Mathematics II (MII)

Gurantor department	Department of Mathematics	Credits	5
Subject guarantor	Mgr. Dagmar Dlouhá, Ph.D.	Subject version guarantor	RNDr. Petr Volný, Ph.D.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	2	Semester	winter
		Study language	Czech
Year of introduction	2019/2020	Year of cancellation
Intended for the faculties	HGF	Intended for study types	Bachelor

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
DLO44	Mgr. Dagmar Dlouhá, Ph.D.
DUB02	RNDr. Viktor Dubovský, Ph.D.
JAR71	Mgr. Marcela Jarošová, Ph.D.
STA50	RNDr. Jana Staňková, Ph.D.
URB0186	RNDr. Zbyněk Urban, Ph.D.
VOL18	RNDr. Jana Volná, Ph.D.
VOL06	RNDr. Petr Volný, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	2+2

Subject aims expressed by acquired skills and competences

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

Teaching methods

Lectures
Individual consultations
Tutorials

Summary

The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three advanced parts of mathematics, according to which the learning material is structured. In Integral Calculus, the main motive is the preparation to general use of definite and indefinite integrals of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Differential Equations is an emphasis on interpretation of the basic procedures for the solution of selected types of differential equations.

Compulsory literature:

Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X http://mdg.vsb.cz/portal/en/Mathematics2.pdf Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1. James, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456.

Recommended literature:

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1. Leon, S., J.: Linear Algebra with Aplications, Macmillan Publishing Company, New York, 1986, ISBN 0-02-369810-1. Moore,C: Math quations and inequalities, Science & Nature, 2014. James, G.: Modern Engineering Mathematics. Addison – Wesley Publishing Company, Wokingham, 1994, ISBN 0-201-18504-5.

Way of continuous check of knowledge in the course of semester

Conditions for obtaining the course-unit credit: participation in exercises, 30% of absences can be excused, submission of programs assigned by the supervisor in the prescribed course, passing of written tests. The student will get 5 b for fulfilling the conditions. The student can get 0 - 15 b for the tests. (The student who gets the credit will be evaluated 5 - 20 b). The condition for participation in the exam is a written credit from the relevant course. The exam consists of a written and an oral part. Students must pass both parts of the exam and achieve the necessary number of points.

E-learning

Other requirements

No more requirements

Prerequisities

Subject code	Abbreviation	Title	Requirement
230-0404	MI	Mathematics I	Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1st Integral calculus: antiderivative and indefinite integral for functions of one variable. 2nd Integration methods - substitution, integration by parts. 3rd Integration of rational functions, irrational functions, trigonometric functions. 4th Definite integrals: basic concepts, properties, Newton-Leibniz rule. 5th Substitution method and integration by parts for the definite integral. 6th Applications of integrals in geometry. 7th Differential calculus for functions of two variables: definition, domain, limits and continuity. 8th Partial derivatives of first order and higher orders. Total differential. 9th The equation of the tangent plane and of the normal. 10th Extrema of functions of two variables. 11th Implicit function and its derivatives. 12th Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear. 13th Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients. 14th Linear differential equations of higher orders.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Credit and Examination	Credit and Examination	100 (100)	51
Credit	Credit	20	5
Examination	Examination	80 (80)	30	3
Písemná zkouška	Written examination	60	25
Ústní zkouška	Oral examination	20	5

Mandatory attendence participation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

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Conditions for subject completion and attendance at the exercises within ISP: Mandatory participation in the course is not required. Other conditions for subject completion will respect the individual needs of the student.

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Form	Study language	Tut. centre	Year	Type of duty
2024/2025	(B0719A290001) Water – Strategic Resource		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0532A330033) Engineering Geodesy		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0532A330034) Geoinformatics		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0532A330040) Applied Geology		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290003) Mineral Economics		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290007) Mining Surveying		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290008) Environmental Protection within Industry		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B1088A330001) Geoscience and Industrial Tourism		P	Czech	Ostrava	2	Optional	study plan
2024/2025	(B0712A290001) Waste Management and Mineral Processing		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290010) Revitalisation of the post-mining landscape		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0532A330033) Engineering Geodesy		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0532A330034) Geoinformatics		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0532A330040) Applied Geology		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0712A290001) Waste Management and Mineral Processing		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0719A290001) Water – Strategic Resource		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290003) Mineral Economics		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290007) Mining Surveying		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290008) Environmental Protection within Industry		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B1088A330001) Geoscience and Industrial Tourism		P	Czech	Ostrava	2	Optional	study plan
2023/2024	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0712A290001) Waste Management and Mineral Processing		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0532A330033) Engineering Geodesy		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0532A330034) Geoinformatics		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0719A290001) Water – Strategic Resource		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0724A290003) Mineral Economics		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0724A290007) Mining Surveying		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B1088A330001) Geoscience and Industrial Tourism		P	Czech	Ostrava	2	Optional	study plan
2022/2023	(B0724A290008) Environmental Protection within Industry		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B2110) Geological Engineering	(2101R003) Geological Engineering	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0532A330040) Applied Geology		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B1316) Geodesy, Cartography and Geoinformatics	(3646R006) Geoinformatics	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B2102) Mineral Raw Materials	(3904R005) Environmental Engineering	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Most	2	Compulsory	study plan
2022/2023	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B2110) Geological Engineering	(2101R003) Geological Engineering	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B1088A330001) Geoscience and Industrial Tourism		P	Czech	Ostrava	2	Optional	study plan
2021/2022	(B0724A290003) Mineral Economics		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0532A330034) Geoinformatics		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0724A290007) Mining Surveying		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0532A330033) Engineering Geodesy		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0719A290001) Water – Strategic Resource		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0712A290001) Waste Management and Mineral Processing		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B2102) Mineral Raw Materials	(3904R005) Environmental Engineering	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B2102) Mineral Raw Materials	(2102R001) Economics and Management in the Field of Raw Materials	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B1316) Geodesy, Cartography and Geoinformatics	(3646R006) Geoinformatics	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B2102) Mineral Raw Materials	(2102R006) Water Technologies and Water Management	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B2110) Geological Engineering	(2101R003) Geological Engineering	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0724A290003) Mineral Economics		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B2102) Mineral Raw Materials	(2102R006) Water Technologies and Water Management	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Most	2	Compulsory	study plan
2020/2021	(B2102) Mineral Raw Materials	(2102R001) Economics and Management in the Field of Raw Materials	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B2102) Mineral Raw Materials	(3902R064) System Engineering in Industry	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B2102) Mineral Raw Materials	(3904R005) Environmental Engineering	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B1088A330001) Geoscience and Industrial Tourism		P	Czech	Ostrava	2	Optional	study plan
2020/2021	(B1316) Geodesy, Cartography and Geoinformatics	(3646R006) Geoinformatics	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B2110) Geological Engineering	(2101R004) Geoscience and Industrial Tourism	P	Czech	Ostrava	2	Optional	study plan
2020/2021	(B2110) Geological Engineering	(2101R004) Geoscience and Industrial Tourism	P	Czech	Most	2	Optional	study plan
2020/2021	(B0712A290001) Waste Management and Mineral Processing		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0719A290001) Water – Strategic Resource		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B0712A290001) Waste Management and Mineral Processing		P	Czech	Ostrava	2	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner
Subject block without study plan - HGF - P - cs	2023/2024	Full-time	Czech				Optional	HGF - Faculty of Mining and Geology	stu. block

Assessment of instruction